大名泛区洪水演进数值模拟

Numerical Simulation of Flood Routing in Daming Flood Detention Basin

利用结构化网格的有限体积法,建立了二维浅水方程的高精度、低计算负荷的数值计算模型。对结构化网格的处理采用一种自适应网格加密方法,提出四叉树的网格构造,以提高网格对地形和水力变化的敏感度。推导出一种具有激波捕捉能力的二维浅水方程的守恒形式,采用单元中心式有限体积离散。方程的离散采用Godunov格式,利用近似Riemann解求解界面通量,并介绍和采用了具有二阶精度的HLLC算法。对在此基础上,建立大名泛区二维洪水演进模型,获取了不同时段的淹没范围栅格图像、不同时刻淹没水深、洪泛区的蓄水量变化过程以及泛区内点的水力要素信息,为泛区的防洪规划和实时洪水预报提供理论参考。

Based on the finite volume method on the structured grids,a two-dimensional numerical model with high precision and low calculation load was established to solve the shallow water equations.In this paper,an adaptive mesh refinement method was adopted and quadtree grids were then generated,which can improve the sensitivity of the grids in terms of the terrain variation and hydraulic change.A scheme of the non-linear shock-capturing shallow water equations in the hyperbolic conservation form was deduced,which discretized the flow variables in the unit center of finite volume.This equation applied the Godunov-type shallow flow solver,and the approximate Riemann solution was used to compute the interface flux.Moreover,the HLLC algorithm with the second order precision was introduced and applied.Then this equation and its solutions were applied to build a two-dimensional flood routing model in the Daming flood detention basin.The submerged scope,submerged depth,storage capacity,and hydraulic characteristics of the points in the basin at different times were obtained.The results can provide the theory references for the flood control planning and real-time flood forecasting in the flood detention basin.